Trailing 69-66 to start the final quarter, Miami outscored Houston 31-19 down the stretch to pull out their sixth win in seven games despite the absences of Dwyane Wade (dislocated finger), Chris Bosh (muscle fatigue) and Mario Chalmers (flu-like symptoms).
James scored 11 points in the final quarter and Norris Cole added 16 as the Heat closed their home schedule with a 28-5 record.
The Rockets, meanwhile, continued their disappointing slide to end the season, officially missing the playoffs with their seventh loss in eight games.
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